How do I increase the 'View Orbit' amount?
The setting of the short cuts can be found in the user preferences, input tab.

Their names are 'view orbit'. The tricky thing is that the values needs to be in radians.

But you can use Python (transparently) to define the value you want in degrees. So to have 22.5 degrees, type "pi/8".



Now you can orbit with the wanted rotation :



Edit : you can also type "radians(22.5)". It seems all the math functions (math Python module, probably) are available.